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SageMath
E = EllipticCurve("hp1")
E.isogeny_class()
Elliptic curves in class 235200hp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
235200.hp1 | 235200hp1 | \([0, -1, 0, -360950333, 2696576261037]\) | \(-46028377077760/1162261467\) | \(-131324038917572113200000000\) | \([]\) | \(61286400\) | \(3.7957\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 235200hp1 has rank \(1\).
Complex multiplication
The elliptic curves in class 235200hp do not have complex multiplication.Modular form 235200.2.a.hp
sage: E.q_eigenform(10)